On (m,n)-ideals in LA-Semigroups

Size: px
Start display at page:

Download "On (m,n)-ideals in LA-Semigroups"

Transcription

1 Applied Mathematical Sciences, Vol. 7, 2013, no. 44, HIKARI Ltd, On (m,n)-ideals in LA-Semigroups Muhammad Akram University of Gujrat Gujrat, Pakistan makram Naveed Yaqoob Quaid-i-Azam University Islamabad, Pakistan Madad Khan COMSATS Institute of Information Technology Abbottabad, Pakistan Copyright c 2013 Muhammad Akram et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The purpose of this paper is to study (m,n)-ideals in LA-semigroups. Some properties of (m,n)-ideals in LA-semigroups and in locally associative LA-semigroups has been provided. Mathematics Subject Classification: 20M10, 20N99 Keywords: LA-semigroups, (m,n)-ideals

2 2188 M. Akram, N. Yaqoob and M. Khan 1 Introduction The concept of (m, n)-ideal of a semigroup was introduced by Lajos [2]. The left almost semigroup (LA-semigroup), was first introduced by Kazim and Naseerudin [1]. Later, Mushtaq [3, 4] and others investigated this idea further and added many useful results to the theory of LA-semigroups. Mushtaq and Yusuf produced useful results [4], on locally associative LA-semigroups in In locally associative LA-semigroups they defined powers of an element and congruences using these powers. In this paper, we discussed some properties of (m,n)-ideals in a locally associative LA-semigroup. 2 Preliminaries and basic definitions Definition 2.1. [1] A groupoid (S, ) is called an LA-semigroup or an AGgroupoid, if it satisfies left invertive law (a b) c =(c b) a, for all a, b, c S. Definition 2.2. [4] An LA-semigroup S is called a locally associative LAsemigroup if and only if (aa)a = a(aa) for all a S. Example 2.3. [4] The set S = {a, b, c}, under defined below in the form of Cayley table is a locally associative LA-semigroup. a b c a c c b b b b b c b b b In [4], the authors define powers of an element in a locally associative LAsemigroup S as follows: a 1 = a, a n+1 = a n a, for n 1. In a locally associative LA-semigroup S with left identity, the results a m a n = a m+n, (a m ) n = a mn and (ab) n = a n b n hold for all a, b S and here m and n are positive integers. In an LA-semigroup S the following medial law holds (ab)(cd) =(ac)(bd) for all a, b, c, d S [1]. In an LA-semigroup S with left identity, the following paramedial law holds (ab)(cd) =(dc)(ba) for all a, b, c, d S. If A and B are any subsets of a locally associative LA-semigroup S then it is easy to prove that (AB) n = A n B n for n 1. Lemma 2.4. [4] If S is an LA-semigroup with left identity, then a(bc) =b(ac), for all a, b, c S. Lemma 2.5. [4] If S is an LA-semigroup with left identity e, then SS = S and S = es = Se.

3 On (m,n)-ideals in LA-semigroups (m, n)-ideals in LA-semigroups A subset A of an LA-semigroup S is called a right (left) ideal of S if AS A (SA A), and is called a two sided ideal if it is both left and right ideal of S. If A is any non-empty subset of an LA-semigroup S, then we define A n =(...((AA)A)...)A, where AA is usual product and n N. Definition 3.1. A subset A of an LA-semigroup S is called an (m, 0)-ideal ((0,n)-ideal) if A m S A (SA n A), for m, n N. Proposition 3.2. Let S be an LA-semigroup with left identity e. Then (1) if A is a proper (m, 0)-ideal of S, then e/ A. (2) if A is a proper (0,n)-ideal of S, then e/ A. Proof. (1) Let A be a proper (m, 0)-ideal of S. Suppose on contrary that e A. Then S = es = e m S A m S A, implies that S A. This is a contradiction to the fact that A is proper. Hence e/ A. (2) Let A be a proper (0,n)-ideal of S. Suppose on contrary that e A. Then by left invertive law S =(ee)s =(Se)e =(Se n )e n (SA n )A n AA n SA n A imply that S A. This is a contradiction to the fact that A is proper. Hence e/ A. Definition 3.3. Let S be an LA-semigroup. An LA-subsemigroup A of S is called an (m, n)-ideal of S, ifa satisfies the condition (A m S)A n A where m, n are non-negative integers (A m is suppressed if m =0). Let A be an LA-subsemigroup of S then we shall say that A is a bi-ideal or (1, 1)-ideal of S if (AS)A A. Proposition 3.4. Let S be an LA-semigroup, B be an LA-subsemigroup of S and let A be an (m, n)-ideal of S. Then the intersection A B is an (m, n)-ideal of the LA-semigroup B. Proof. The intersection A B evidently is an LA-subsemigroup of S. We have to show that A B is an (m, n)-ideal of B, for this ((A B) m B)(A B) n (A m S)A n A, (1) because A is an (m, n)-ideal of S. Secondly ((A B) m B)(A B) n (B m B)B n B. (2) Therefore (1) and (2) implies that ((A B) m B)(A B) n A B. Thus the intersection A B is an (m, n)-ideal of B.

4 2190 M. Akram, N. Yaqoob and M. Khan Theorem 3.5. Let {A i : i I} be a family of (m, n)-ideals of an LAsemigroup S. Then B = n A i is an (m, n)-ideal of S. Proof. Let {A i : i I} be a family of (m, n)-ideals of an LA-semigroup S. We know that the intersection of LA-subsemigroups is an LA-subsemigroup, now to show that B = n A i is an (m, n)-ideal of S. Here we need only to show that (B m S)B n B. Let x (B m S)B n. Then x =(a m 1 s)a n 2 for some a m 1,a n 2 B and s S. Thus for any arbitrary i I as a m 1,an 2 B i. So x (Bi ms)bn i. Since B i is an (m, n)-ideal so (Bi ms)bn i B i and therefore x B i. Since i was chosen arbitrarily so x B i for all i I and hence x B. So, (B m S)B n B and hence B = n A i is an (m, n)-ideal of S. Definition 3.6. An element a of an LA-semigroup S is called idempotent if aa = a. A subset I of an LA-semigroup S is called idempotent if all of its elements are idempotent. Theorem 3.7. If B is an idempotent (m, m)-ideal of a locally associative LA-semigroup S with left identity, then B is an (m, 0)-ideal and a (0,m)-ideal of S. Proof. By using left invertive law and paramedial law, we obtain B m S = (B 2 ) m S =(B m ) 2 S =(B m B m )S =(SB m )B m =(SB m )(B m B m ) = (B m B m )(B m S)=((B m S)B m )B m BB m B. This shows that B is an (m, 0)-ideal of S. Similarly, by using Lemma 2.4 and medial law, we get SB m = S(B m B m )=(B m B m )(SB m )=(B m S)(B m B m )=(B m S)B m B. This shows that B is a (0,m)-ideal of S. Hence B is an (m, 0)-ideal and a (0,m)-ideal of S. Proposition 3.8. Let A be an LA-subsemigroup of a locally associative LAsemigroup S with left identity. If A is a (0,m)-ideal and B is an (m, n)-ideal of S, then BA is an (m, n)-ideal of S. Proof. Using medial law, we get (BA)(BA) =(BB)(AA) BA. Now by left invertive law ((BA) m S)(BA) n = ((B m A m )S)(B n A n )=((SA m )B m )(B n A n ) = ((B n A n )B m )(SA m )=((B m A n )B n )(SA m ) ((B m S)B n )(SA m ) BA. Hence BA is an (m, n)-ideal of S.

5 On (m,n)-ideals in LA-semigroups 2191 Proposition 3.9. The product of two (m, n)-ideals of a locally associative LA-semigroup S with left identity is an (m, n)-ideal of S. Proof. By medial law, we get (AB)(AB) = (AA)(BB) AB. Now using medial law and Lemma 2.5, we get ((AB) m S)(AB) n = ((A m B m )S)(A n B n )=((A m B m )(SS))(A n B n ) = ((A m S)(B m S))(A n B n )=((A m S)A n )((B m S)B n ) AB. Hence AB is an (m, n)-ideal of S. Theorem Let A and B be LA-subsemigroups of a locally associative LA-semigroup S. IfA is an (m, 0)-ideal and B is a (0,n)-ideal of S, then the product AB is an (m, n)-ideal of S if AB A. Proof. By medial law we get (AB)(AB) =(AA)(BB) AB. This shows that AB is an LA-subsemigroup. Now ((AB) m S)(AB) n (A m S)(A n B n ) A(SB n ) AB. Hence the product AB is an (m, n)-ideal of S. References [1] M.A. Kazim and M. Naseerudin, On almost-semigroup, Aligarh Bull. Math., 2 (1972), 1-7. [2] S. Lajos, Generalized ideals in semigroups, Acta Sci. Math., 22 (1961), [3] Q. Mushtaq and S.M. Yusuf, On LA-semigroups, Aligarh Bull. Math., 8 (1978), [4] Q. Mushtaq and S.M. Yusuf, On locally associative LA-semigroups, J. Nat. Sci. Math., 19 (1979), [5] N. Yaqoob, M. Aslam, B. Davvaz and A.B. Saeid, On rough (m,n) bi- Γ-hyperideals in Γ-semihypergroups, U.P.B. Scientific Bulletin. Series A, 75(1) (2013) [6] M. Aslam, M. Shabir, N. Yaqoob and A. Shabir, On rough (m,n)-bi-ideals and generalized rough (m,n)-bi-ideals in semigroups, Ann. Fuzzy Math. Inform., 2(2) (2011) Received: January 14, 2013

ON (m, n)-ideals OF AN ORDERED ABEL-GRASSMANN GROUPOID. Faisal Yousafzai, Asad Khan, and Aiyared Iampan

ON (m, n)-ideals OF AN ORDERED ABEL-GRASSMANN GROUPOID. Faisal Yousafzai, Asad Khan, and Aiyared Iampan Korean J. Math. 23 (2015), No. 3, pp. 357 370 http://dx.doi.org/10.11568/kjm.2015.23.3.357 ON (m, n)-ideals OF AN ORDERED ABEL-GRASSMANN GROUPOID Faisal Yousafzai, Asad Khan, and Aiyared Iampan Abstract.

More information

A note on an Abel-Grassmann's 3-band. 1. Introduction

A note on an Abel-Grassmann's 3-band. 1. Introduction Quasigroups and Related Systems 15 (2007), 295 301 A note on an Abel-Grassmann's 3-band Qaiser Mushtaq and Madad Khan Abstract An Abel-Grassmann's groupoid is discussed in several papers. In this paper

More information

On Uni-soft (Quasi) Ideals of AG-groupoids

On Uni-soft (Quasi) Ideals of AG-groupoids Applied Mathematical Sciences, Vol. 8, 2014, no. 12, 589-600 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.310583 On Uni-soft (Quasi) Ideals of AG-groupoids Muhammad Sarwar and Abid

More information

Some Structural Properties of AG-Groups

Some Structural Properties of AG-Groups International Mathematical Forum, Vol. 6, 2011, no. 34, 1661-1667 Some Structural Properties of AG-Groups Muhammad Shah and Asif Ali Department of Mathematics Quaid-i-Azam University Islamabad, Pakistan

More information

Characterizations of Intra-Regular Left Almost Semigroups by Their Fuzzy Ideals

Characterizations of Intra-Regular Left Almost Semigroups by Their Fuzzy Ideals Characterizations of Intra-Regular Left Almost Semigroups by Their Fuzzy Ideals Madad Khan Department of Mathematics, COMSATS Institute of Information Technology Abbottabad, Pakistan E-mail: madadmath@yahoo.com

More information

DECOMPOSITION OF LOCALLY ASSOCIATIVE Γ-AG-GROUPOIDS 1

DECOMPOSITION OF LOCALLY ASSOCIATIVE Γ-AG-GROUPOIDS 1 Novi Sad J. Math. Vol. 43, No. 1, 2013, 1-8 DECOMPOSITION OF LOCALLY ASSOCIATIVE Γ-AG-GROUPOIDS 1 Tariq Shah 2 and Inayatur-Rehman 3 Abstract. It is well known that power associativity and congruences

More information

arxiv: v1 [math.gr] 20 Mar 2014

arxiv: v1 [math.gr] 20 Mar 2014 SOME GENERAL PROPERTIES OF LAD AND RAD AG-GROUPOIDS arxiv:1403.5218v1 [math.gr] 20 Mar 2014 M. RASHAD A, I. AHMAD A,, AND M. SHAH 2010 Mathematics Subject Classification: 20N02 Abstract. A groupoid that

More information

On Γ-Ideals and Γ-Bi-Ideals in Γ-AG-Groupoids

On Γ-Ideals and Γ-Bi-Ideals in Γ-AG-Groupoids International Journal of Algebra, Vol. 4, 2010, no. 6, 267-276 On Γ-Ideals and Γ-Bi-Ideals in Γ-AG-Groupoids Tariq Shah and Inayatur Rehman Department of Mathematics, Quaid-i-Azam University, Islamabad-Pakistan

More information

arxiv: v1 [math.gr] 21 Feb 2014

arxiv: v1 [math.gr] 21 Feb 2014 LEFT TRANSITIVE AG-GROUPOIDS M. RASHAD, I. AHMAD, AND M. SHAH arxiv:1402.5296v1 [math.gr] 21 Feb 2014 Abstract. An AG-groupoid is an algebraic structure that satisfies the left invertive law: (ab)c = (cb)a.

More information

arxiv: v1 [math.gr] 5 Oct 2015

arxiv: v1 [math.gr] 5 Oct 2015 ON CYCLIC ASSOCIATIVE ABEL-GRASSMAN GROUPOIDS M. IQBAL A, I. AHMAD A, M. SHAH B, AND M. IRFAN ALI C arxiv:1510.01316v1 [math.gr] 5 Oct 2015 Abstract. A new subclass of AG-groupoids, so called, cyclic associative

More information

Songklanakarin Journal of Science and Technology SJST R1 Yaqoob. Hyperideals and Hypersystems in LA-hyperrings

Songklanakarin Journal of Science and Technology SJST R1 Yaqoob. Hyperideals and Hypersystems in LA-hyperrings Songklanakarin Journal of Science and Technology SJST-0-0.R Yaqoob Hyperideals and Hypersystems in LA-hyperrings Journal: Songklanakarin Journal of Science and Technology Manuscript ID SJST-0-0.R Manuscript

More information

Characterizations of Abel-Grassmann's Groupoids by Intuitionistic Fuzzy Ideals

Characterizations of Abel-Grassmann's Groupoids by Intuitionistic Fuzzy Ideals World pplied Sciences Journal 7 (1): 154-1530, 013 ISSN 1818-495 IDOSI Publications, 013 DOI: 10.589/idosi.wasj.013.7.1.67 Characterizations of bel-grassmann's Groupoids by Intuitionistic Fuzzy Ideals

More information

VOL. 2, NO. 2, February 2012 ISSN ARPN Journal of Systems and Software AJSS Journal. All rights reserved

VOL. 2, NO. 2, February 2012 ISSN ARPN Journal of Systems and Software AJSS Journal. All rights reserved Some fuzzifications in ordered AG**-groupoid ¹ Faisal, ² Kifayat Ullah, ³ Abdul Haseeb, ⁴ Naveed Yaqoob Department of Mathematics, COMSATS Institute of Information Technology Abbottabad, K. P. K., Pakistan

More information

Hyperideals and hypersystems in LA-hyperrings

Hyperideals and hypersystems in LA-hyperrings Songklanakarin J. Sci. Technol. 39 (5), 651-657, Sep. - Oct. 017 http://www.sjst.psu.ac.th Original Article Hyperideals and hypersystems in LA-hyperrings Inayatur Rehman 1, Naveed Yaqoob *, and Shah Nawaz

More information

On relations between right alternative and nuclear square AG-groupoids

On relations between right alternative and nuclear square AG-groupoids International Mathematical Forum, Vol. 8, 2013, no. 5, 237-243 On relations between right alternative and nuclear square AG-groupoids Muhammad Rashad, Imtiaz Ahmad, Amanullah Department of Mathematics

More information

Left almost semigroups dened by a free algebra. 1. Introduction

Left almost semigroups dened by a free algebra. 1. Introduction Quasigroups and Related Systems 16 (2008), 69 76 Left almost semigroups dened by a free algebra Qaiser Mushtaq and Muhammad Inam Abstract We have constructed LA-semigroups through a free algebra, and the

More information

Neutrosophic Left Almost Semigroup

Neutrosophic Left Almost Semigroup 18 Neutrosophic Left Almost Semigroup Mumtaz Ali 1*, Muhammad Shabir 2, Munazza Naz 3 and Florentin Smarandache 4 1,2 Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000,Pakistan. E-mail:

More information

Right Derivations on Semirings

Right Derivations on Semirings International Mathematical Forum, Vol. 8, 2013, no. 32, 1569-1576 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2013.38150 Right Derivations on Semirings S. P. Nirmala Devi Department of

More information

Songklanakarin Journal of Science and Technology SJST R1 Yaqoob

Songklanakarin Journal of Science and Technology SJST R1 Yaqoob On (, qk)-intuitionistic (fuzzy ideals, fuzzy soft ideals) of subtraction algebras Journal: Songklanakarin Journal of Science Technology Manuscript ID: SJST-0-00.R Manuscript Type: Original Article Date

More information

Prime Hyperideal in Multiplicative Ternary Hyperrings

Prime Hyperideal in Multiplicative Ternary Hyperrings International Journal of Algebra, Vol. 10, 2016, no. 5, 207-219 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2016.6320 Prime Hyperideal in Multiplicative Ternary Hyperrings Md. Salim Department

More information

arxiv: v1 [math.ra] 25 May 2013

arxiv: v1 [math.ra] 25 May 2013 Quasigroups and Related Systems 20 (2012), 203 209 Congruences on completely inverse AG -groupoids Wieslaw A. Dudek and Roman S. Gigoń arxiv:1305.6858v1 [math.ra] 25 May 2013 Abstract. By a completely

More information

Diophantine Equations. Elementary Methods

Diophantine Equations. Elementary Methods International Mathematical Forum, Vol. 12, 2017, no. 9, 429-438 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.7223 Diophantine Equations. Elementary Methods Rafael Jakimczuk División Matemática,

More information

On Symmetric Bi-Multipliers of Lattice Implication Algebras

On Symmetric Bi-Multipliers of Lattice Implication Algebras International Mathematical Forum, Vol. 13, 2018, no. 7, 343-350 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2018.8423 On Symmetric Bi-Multipliers of Lattice Implication Algebras Kyung Ho

More information

Some Results About Generalized BCH-Algebras

Some Results About Generalized BCH-Algebras International Journal of Algebra, Vol. 11, 2017, no. 5, 231-246 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ija.2017.712 Some Results About Generalized BCH-Algebras Muhammad Anwar Chaudhry 1

More information

A GENERALIZATION OF BI IDEALS IN SEMIRINGS

A GENERALIZATION OF BI IDEALS IN SEMIRINGS BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874, ISSN (o) 2303-4955 www.imvibl.org /JOURNALS / BULLETIN Vol. 8(2018), 123-133 DOI: 10.7251/BIMVI1801123M Former BULLETIN

More information

Strongly Regular Congruences on E-inversive Semigroups

Strongly Regular Congruences on E-inversive Semigroups International Mathematical Forum, Vol. 10, 2015, no. 1, 47-56 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2015.411188 Strongly Regular Congruences on E-inversive Semigroups Hengwu Zheng

More information

International Journal of Algebra, Vol. 7, 2013, no. 3, HIKARI Ltd, On KUS-Algebras. and Areej T.

International Journal of Algebra, Vol. 7, 2013, no. 3, HIKARI Ltd,   On KUS-Algebras. and Areej T. International Journal of Algebra, Vol. 7, 2013, no. 3, 131-144 HIKARI Ltd, www.m-hikari.com On KUS-Algebras Samy M. Mostafa a, Mokhtar A. Abdel Naby a, Fayza Abdel Halim b and Areej T. Hameed b a Department

More information

Prime and Semiprime Bi-ideals in Ordered Semigroups

Prime and Semiprime Bi-ideals in Ordered Semigroups International Journal of Algebra, Vol. 7, 2013, no. 17, 839-845 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2013.310105 Prime and Semiprime Bi-ideals in Ordered Semigroups R. Saritha Department

More information

Canonical Commutative Ternary Groupoids

Canonical Commutative Ternary Groupoids International Journal of Algebra, Vol. 11, 2017, no. 1, 35-42 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ija.2017.714 Canonical Commutative Ternary Groupoids Vesna Celakoska-Jordanova Faculty

More information

Axioms of Countability in Generalized Topological Spaces

Axioms of Countability in Generalized Topological Spaces International Mathematical Forum, Vol. 8, 2013, no. 31, 1523-1530 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2013.37142 Axioms of Countability in Generalized Topological Spaces John Benedict

More information

A Generalization of p-rings

A Generalization of p-rings International Journal of Algebra, Vol. 9, 2015, no. 8, 395-401 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2015.5848 A Generalization of p-rings Adil Yaqub Department of Mathematics University

More information

On generalized fuzzy sets in ordered LA-semihypergroups

On generalized fuzzy sets in ordered LA-semihypergroups Proceedings of the Estonian Academy of Sciences, 2019, 68, 1, 43 54 https://doi.org/10.3176/proc.2019.1.06 Available online at www.eap.ee/proceedings On generalized fuzzy sets in ordered LA-semihypergroups

More information

Caristi-type Fixed Point Theorem of Set-Valued Maps in Metric Spaces

Caristi-type Fixed Point Theorem of Set-Valued Maps in Metric Spaces International Journal of Mathematical Analysis Vol. 11, 2017, no. 6, 267-275 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2017.717 Caristi-type Fixed Point Theorem of Set-Valued Maps in Metric

More information

SANDWICH SETS AND CONGRUENCES IN COMPLETELY INVERSE AG -GROUPOIDS

SANDWICH SETS AND CONGRUENCES IN COMPLETELY INVERSE AG -GROUPOIDS ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS N. 39 2018 (822 838) 822 SANDWICH SETS AND CONGRUENCES IN COMPLETELY INVERSE AG -GROUPOIDS Waqar Khan School of Mathematics and Statistics Southwest University

More information

β Baire Spaces and β Baire Property

β Baire Spaces and β Baire Property International Journal of Contemporary Mathematical Sciences Vol. 11, 2016, no. 5, 211-216 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2016.612 β Baire Spaces and β Baire Property Tugba

More information

INTUITIONISTIC FUZZY IDEALS OF LA-SEMIGROUPS.

INTUITIONISTIC FUZZY IDEALS OF LA-SEMIGROUPS. INTUITIONISTIC FUZZY IDEALS OF LA-SEMIGROUPS. MUHAMMAD ASLAM AND SALEEM ABDULLAH Abstract. e consider the intuitionistic fuzzi cation of the concept of several ideals in LA-semigroup S, investigate some

More information

A Note on UNAR LA-Semigroup

A Note on UNAR LA-Semigroup Punjab University Journal of Mathematics (ISSN 1016-2526) Vol. 50(3)(2018) pp. 113-121 A Note on UNAR LA-Semigroup Muhammad Rashad Department of Mathematics, University of Malakand, Pakistan, Email: rashad@uom.edu.pk

More information

International Mathematical Forum, Vol. 9, 2014, no. 36, HIKARI Ltd,

International Mathematical Forum, Vol. 9, 2014, no. 36, HIKARI Ltd, International Mathematical Forum, Vol. 9, 2014, no. 36, 1751-1756 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.411187 Generalized Filters S. Palaniammal Department of Mathematics Thiruvalluvar

More information

Generalized Boolean and Boolean-Like Rings

Generalized Boolean and Boolean-Like Rings International Journal of Algebra, Vol. 7, 2013, no. 9, 429-438 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2013.2894 Generalized Boolean and Boolean-Like Rings Hazar Abu Khuzam Department

More information

Direct Product of BF-Algebras

Direct Product of BF-Algebras International Journal of Algebra, Vol. 10, 2016, no. 3, 125-132 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2016.614 Direct Product of BF-Algebras Randy C. Teves and Joemar C. Endam Department

More information

Solving Homogeneous Systems with Sub-matrices

Solving Homogeneous Systems with Sub-matrices Pure Mathematical Sciences, Vol 7, 218, no 1, 11-18 HIKARI Ltd, wwwm-hikaricom https://doiorg/112988/pms218843 Solving Homogeneous Systems with Sub-matrices Massoud Malek Mathematics, California State

More information

Locating Chromatic Number of Banana Tree

Locating Chromatic Number of Banana Tree International Mathematical Forum, Vol. 12, 2017, no. 1, 39-45 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.610138 Locating Chromatic Number of Banana Tree Asmiati Department of Mathematics

More information

ON SOME SEMIGROUPS GENERATED FROM CAYLEY FUNCTIONS LEJO J. MANAVALAN, P.G. ROMEO

ON SOME SEMIGROUPS GENERATED FROM CAYLEY FUNCTIONS LEJO J. MANAVALAN, P.G. ROMEO Available online at http://scikorg J Semigroup Theory Appl 2018, 2018:5 https://doiorg/1028919/jsta/3562 ISSN: 2051-2937 ON SOME SEMIGROUPS GENERATED FROM CAYLEY FUNCTIONS LEJO J MANAVALAN, PG ROMEO Department

More information

Enumerating AG-Groups with a Study of Smaradache AG-Groups

Enumerating AG-Groups with a Study of Smaradache AG-Groups International Mathematical Forum, Vol. 6, 2011, no. 62, 3079-3086 Enumerating AG-Groups with a Study of Smaradache AG-Groups Muhammad Shah 1 Department of Mathematics Quaid-i-Azam University, Pakistan

More information

r-ideals of Commutative Semigroups

r-ideals of Commutative Semigroups International Journal of Algebra, Vol. 10, 2016, no. 11, 525-533 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ija.2016.61276 r-ideals of Commutative Semigroups Muhammet Ali Erbay Department of

More information

Semigroup presentations via boundaries in Cayley graphs 1

Semigroup presentations via boundaries in Cayley graphs 1 Semigroup presentations via boundaries in Cayley graphs 1 Robert Gray University of Leeds BMC, Newcastle 2006 1 (Research conducted while I was a research student at the University of St Andrews, under

More information

A New Generalization of Fuzzy Ideals of Ternary Semigroups

A New Generalization of Fuzzy Ideals of Ternary Semigroups Appl Math Inf Sci 9, No 3, 1623-1637 2015 1623 Applied Mathematics & Information Sciences An International Journal http://dxdoiorg/1012785/amis/090359 A New Generalization of Fuzzy Ideals of Ternary Semigroups

More information

Stability of a Functional Equation Related to Quadratic Mappings

Stability of a Functional Equation Related to Quadratic Mappings International Journal of Mathematical Analysis Vol. 11, 017, no., 55-68 HIKARI Ltd, www.m-hikari.com https://doi.org/10.1988/ijma.017.610116 Stability of a Functional Equation Related to Quadratic Mappings

More information

arxiv: v2 [math.gr] 10 Feb 2015

arxiv: v2 [math.gr] 10 Feb 2015 ENUMERATION OF BI-COMMUTATIVE-AG-GROUPOIDS M. RASHAD A, I. AHMAD A,, M. SHAH B, AND A. B. SAEID C arxiv:1403.5393v2 [math.gr] 10 Feb 2015 Abstract. We introduce left, right and bi-commutative AG-groupoids.

More information

Complete Ideal and n-ideal of B-algebra

Complete Ideal and n-ideal of B-algebra Applied Mathematical Sciences, Vol. 11, 2017, no. 35, 1705-1713 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.75159 Complete Ideal and n-ideal of B-algebra Habeeb Kareem Abdullah University

More information

Secure Weakly Connected Domination in the Join of Graphs

Secure Weakly Connected Domination in the Join of Graphs International Journal of Mathematical Analysis Vol. 9, 2015, no. 14, 697-702 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.519 Secure Weakly Connected Domination in the Join of Graphs

More information

On Strong Alt-Induced Codes

On Strong Alt-Induced Codes Applied Mathematical Sciences, Vol. 12, 2018, no. 7, 327-336 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2018.8113 On Strong Alt-Induced Codes Ngo Thi Hien Hanoi University of Science and

More information

On the Power of Standard Polynomial to M a,b (E)

On the Power of Standard Polynomial to M a,b (E) International Journal of Algebra, Vol. 10, 2016, no. 4, 171-177 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2016.6214 On the Power of Standard Polynomial to M a,b (E) Fernanda G. de Paula

More information

Generalized Derivation on TM Algebras

Generalized Derivation on TM Algebras International Journal of Algebra, Vol. 7, 2013, no. 6, 251-258 HIKARI Ltd, www.m-hikari.com Generalized Derivation on TM Algebras T. Ganeshkumar Department of Mathematics M.S.S. Wakf Board College Madurai-625020,

More information

Regular Generalized Star b-continuous Functions in a Bigeneralized Topological Space

Regular Generalized Star b-continuous Functions in a Bigeneralized Topological Space International Journal of Mathematical Analysis Vol. 9, 2015, no. 16, 805-815 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.5230 Regular Generalized Star b-continuous Functions in a

More information

Quotient and Homomorphism in Krasner Ternary Hyperrings

Quotient and Homomorphism in Krasner Ternary Hyperrings International Journal of Mathematical Analysis Vol. 8, 2014, no. 58, 2845-2859 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.410316 Quotient and Homomorphism in Krasner Ternary Hyperrings

More information

Homomorphism on Fuzzy Generalised Lattices

Homomorphism on Fuzzy Generalised Lattices International Journal of Contemporary Mathematical Sciences Vol. 11, 2016, no. 6, 275-279 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2016.6525 Homomorphism on Fuzzy Generalised Lattices

More information

Restrained Weakly Connected Independent Domination in the Corona and Composition of Graphs

Restrained Weakly Connected Independent Domination in the Corona and Composition of Graphs Applied Mathematical Sciences, Vol. 9, 2015, no. 20, 973-978 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.4121046 Restrained Weakly Connected Independent Domination in the Corona and

More information

NOWADAYS we are facing so many problems in practical

NOWADAYS we are facing so many problems in practical INTERNATIONAL JOURNAL OF MATHEMATICS AND SCIENTIFIC COMPUTING (ISSN: 2231-5330), VOL. 5, NO. 1, 2015 60 Uni-Soft Ideals of Ternary Semigroups Abid Khan and Muhammad Sarwar Abstract In this paper we introduce

More information

Endo-prime Submodules in Endo-multiplication Modules

Endo-prime Submodules in Endo-multiplication Modules International Mathematical Forum, Vol. 9, 2014, no. 27, 1321-1332 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.47139 Endo-prime Submodules in Endo-multiplication Modules Indah Emilia

More information

Sums of Tribonacci and Tribonacci-Lucas Numbers

Sums of Tribonacci and Tribonacci-Lucas Numbers International Journal of Mathematical Analysis Vol. 1, 018, no. 1, 19-4 HIKARI Ltd, www.m-hikari.com https://doi.org/10.1988/ijma.018.71153 Sums of Tribonacci Tribonacci-Lucas Numbers Robert Frontczak

More information

A Novel Approach: Soft Groups

A Novel Approach: Soft Groups International Journal of lgebra, Vol 9, 2015, no 2, 79-83 HIKRI Ltd, wwwm-hikaricom http://dxdoiorg/1012988/ija2015412121 Novel pproach: Soft Groups K Moinuddin Faculty of Mathematics, Maulana zad National

More information

Characterization of Weakly Primary Ideals over Non-commutative Rings

Characterization of Weakly Primary Ideals over Non-commutative Rings International Mathematical Forum, Vol. 9, 2014, no. 34, 1659-1667 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.49155 Characterization of Weakly Primary Ideals over Non-commutative Rings

More information

On a Certain Representation in the Pairs of Normed Spaces

On a Certain Representation in the Pairs of Normed Spaces Applied Mathematical Sciences, Vol. 12, 2018, no. 3, 115-119 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2018.712362 On a Certain Representation in the Pairs of ormed Spaces Ahiro Hoshida

More information

Fuzzy soft set approach to ideal theory of regular AG-groupoids

Fuzzy soft set approach to ideal theory of regular AG-groupoids DOI: 10.1515/auom-2016-0015 An. Şt. Univ. Ovidius Constanţa Vol. 24(1),2016, 263 288 Fuzzy soft set approach to ideal theory of regular AG-groupoids Feng Feng, Madad Khan, Violeta Leoreanu-Fotea, aima

More information

Intuitionistic Fuzzy Bi-Ideals of Ternary Semigroups

Intuitionistic Fuzzy Bi-Ideals of Ternary Semigroups International Mathematical Forum, Vol. 7, 2012, no. 8, 385-389 Intuitionistic Fuzzy Bi-Ideals of Ternary Semigroups S. Lekkoksung Rajamangala University of Technology Isan Khon Kaen Campus, Thail Lekkoksung

More information

Secure Weakly Convex Domination in Graphs

Secure Weakly Convex Domination in Graphs Applied Mathematical Sciences, Vol 9, 2015, no 3, 143-147 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/1012988/ams2015411992 Secure Weakly Convex Domination in Graphs Rene E Leonida Mathematics Department

More information

A Short Note on Universality of Some Quadratic Forms

A Short Note on Universality of Some Quadratic Forms International Mathematical Forum, Vol. 8, 2013, no. 12, 591-595 HIKARI Ltd, www.m-hikari.com A Short Note on Universality of Some Quadratic Forms Cherng-tiao Perng Department of Mathematics Norfolk State

More information

Toric Deformation of the Hankel Variety

Toric Deformation of the Hankel Variety Applied Mathematical Sciences, Vol. 10, 2016, no. 59, 2921-2925 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.6248 Toric Deformation of the Hankel Variety Adelina Fabiano DIATIC - Department

More information

Double Total Domination on Generalized Petersen Graphs 1

Double Total Domination on Generalized Petersen Graphs 1 Applied Mathematical Sciences, Vol. 11, 2017, no. 19, 905-912 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.7114 Double Total Domination on Generalized Petersen Graphs 1 Chengye Zhao 2

More information

A Family of Optimal Multipoint Root-Finding Methods Based on the Interpolating Polynomials

A Family of Optimal Multipoint Root-Finding Methods Based on the Interpolating Polynomials Applied Mathematical Sciences, Vol. 8, 2014, no. 35, 1723-1730 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.4127 A Family of Optimal Multipoint Root-Finding Methods Based on the Interpolating

More information

µs p -Sets and µs p -Functions

µs p -Sets and µs p -Functions International Journal of Mathematical Analysis Vol. 9, 2015, no. 11, 499-508 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.412401 µs p -Sets and µs p -Functions Philip Lester Pillo

More information

A NOVEL VIEW OF ROUGH SOFT SEMIGROUPS BASED ON FUZZY IDEALS. Qiumei Wang Jianming Zhan Introduction

A NOVEL VIEW OF ROUGH SOFT SEMIGROUPS BASED ON FUZZY IDEALS. Qiumei Wang Jianming Zhan Introduction italian journal of pure and applied mathematics n. 37 2017 (673 686) 673 A NOVEL VIEW OF ROUGH SOFT SEMIGROUPS BASED ON FUZZY IDEALS Qiumei Wang Jianming Zhan 1 Department of Mathematics Hubei University

More information

Some Properties of D-sets of a Group 1

Some Properties of D-sets of a Group 1 International Mathematical Forum, Vol. 9, 2014, no. 21, 1035-1040 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.45104 Some Properties of D-sets of a Group 1 Joris N. Buloron, Cristopher

More information

When is the Ring of 2x2 Matrices over a Ring Galois?

When is the Ring of 2x2 Matrices over a Ring Galois? International Journal of Algebra, Vol. 7, 2013, no. 9, 439-444 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2013.3445 When is the Ring of 2x2 Matrices over a Ring Galois? Audrey Nelson Department

More information

Some Range-Kernel Orthogonality Results for Generalized Derivation

Some Range-Kernel Orthogonality Results for Generalized Derivation International Journal of Contemporary Mathematical Sciences Vol. 13, 2018, no. 3, 125-131 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2018.8412 Some Range-Kernel Orthogonality Results for

More information

Fibonacci sequences in groupoids

Fibonacci sequences in groupoids Han et al. Advances in Difference Equations 22, 22:9 http://www.advancesindifferenceequations.com/content/22//9 RESEARCH Open Access Fibonacci sequences in groupoids Jeong Soon Han, Hee Sik Kim 2* and

More information

Hyers-Ulam-Rassias Stability of a Quadratic-Additive Type Functional Equation on a Restricted Domain

Hyers-Ulam-Rassias Stability of a Quadratic-Additive Type Functional Equation on a Restricted Domain Int. Journal of Math. Analysis, Vol. 7, 013, no. 55, 745-75 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ijma.013.394 Hyers-Ulam-Rassias Stability of a Quadratic-Additive Type Functional Equation

More information

Regular Weakly Star Closed Sets in Generalized Topological Spaces 1

Regular Weakly Star Closed Sets in Generalized Topological Spaces 1 Applied Mathematical Sciences, Vol. 9, 2015, no. 79, 3917-3929 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.53237 Regular Weakly Star Closed Sets in Generalized Topological Spaces 1

More information

Join Reductions and Join Saturation Reductions of Abstract Knowledge Bases 1

Join Reductions and Join Saturation Reductions of Abstract Knowledge Bases 1 International Journal of Contemporary Mathematical Sciences Vol. 12, 2017, no. 3, 109-115 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2017.7312 Join Reductions and Join Saturation Reductions

More information

The Greatest Common Divisor of k Positive Integers

The Greatest Common Divisor of k Positive Integers International Mathematical Forum, Vol. 3, 208, no. 5, 25-223 HIKARI Ltd, www.m-hiari.com https://doi.org/0.2988/imf.208.822 The Greatest Common Divisor of Positive Integers Rafael Jaimczu División Matemática,

More information

Abel-Grassmann s bands. 1. Introduction

Abel-Grassmann s bands. 1. Introduction Quasigroups and Related Systems 11 (2004), 95 101 Abel-Grassmann s bands Petar V. Protić and Nebojša Stevanović Abstract Abel-Grassmann s groupoids or shortly AG-groupoids have been considered in a number

More information

On Annihilator Small Intersection Graph

On Annihilator Small Intersection Graph International Journal of Contemporary Mathematical Sciences Vol. 12, 2017, no. 7, 283-289 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2017.7931 On Annihilator Small Intersection Graph Mehdi

More information

Restrained Independent 2-Domination in the Join and Corona of Graphs

Restrained Independent 2-Domination in the Join and Corona of Graphs Applied Mathematical Sciences, Vol. 11, 2017, no. 64, 3171-3176 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.711343 Restrained Independent 2-Domination in the Join and Corona of Graphs

More information

A Class of Z4C-Groups

A Class of Z4C-Groups Applied Mathematical Sciences, Vol. 9, 2015, no. 41, 2031-2035 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.4121008 A Class of Z4C-Groups Jinshan Zhang 1 School of Science Sichuan University

More information

Unit Group of Z 2 D 10

Unit Group of Z 2 D 10 International Journal of Algebra, Vol. 9, 2015, no. 4, 179-183 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2015.5420 Unit Group of Z 2 D 10 Parvesh Kumari Department of Mathematics Indian

More information

of a Two-Operator Product 1

of a Two-Operator Product 1 Applied Mathematical Sciences, Vol. 7, 2013, no. 130, 6465-6474 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2013.39501 Reverse Order Law for {1, 3}-Inverse of a Two-Operator Product 1 XUE

More information

Some Reviews on Ranks of Upper Triangular Block Matrices over a Skew Field

Some Reviews on Ranks of Upper Triangular Block Matrices over a Skew Field International Mathematical Forum, Vol 13, 2018, no 7, 323-335 HIKARI Ltd, wwwm-hikaricom https://doiorg/1012988/imf20188528 Some Reviews on Ranks of Upper Triangular lock Matrices over a Skew Field Netsai

More information

Supra g-closed Sets in Supra Bitopological Spaces

Supra g-closed Sets in Supra Bitopological Spaces International Mathematical Forum, Vol. 3, 08, no. 4, 75-8 HIKARI Ltd, www.m-hikari.com https://doi.org/0.988/imf.08.8 Supra g-closed Sets in Supra Bitopological Spaces R. Gowri Department of Mathematics

More information

Rainbow Connection Number of the Thorn Graph

Rainbow Connection Number of the Thorn Graph Applied Mathematical Sciences, Vol. 8, 2014, no. 128, 6373-6377 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.48633 Rainbow Connection Number of the Thorn Graph Yixiao Liu Department

More information

Fuzzy Sequences in Metric Spaces

Fuzzy Sequences in Metric Spaces Int. Journal of Math. Analysis, Vol. 8, 2014, no. 15, 699-706 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4262 Fuzzy Sequences in Metric Spaces M. Muthukumari Research scholar, V.O.C.

More information

On a Boundary-Value Problem for Third Order Operator-Differential Equations on a Finite Interval

On a Boundary-Value Problem for Third Order Operator-Differential Equations on a Finite Interval Applied Mathematical Sciences, Vol. 1, 216, no. 11, 543-548 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.12988/ams.216.512743 On a Boundary-Value Problem for Third Order Operator-Differential Equations

More information

The C 8 -Group Having Five Maximal Subgroups of Index 2 and Three of Index 3

The C 8 -Group Having Five Maximal Subgroups of Index 2 and Three of Index 3 International Journal of Algebra, Vol. 11, 2017, no. 8, 375-379 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ija.2017.71047 The C 8 -Group Having Five Maximal Subgroups of Index 2 and Three of

More information

Solvability of System of Generalized Vector Quasi-Equilibrium Problems

Solvability of System of Generalized Vector Quasi-Equilibrium Problems Applied Mathematical Sciences, Vol. 8, 2014, no. 53, 2627-2633 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.43183 Solvability of System of Generalized Vector Quasi-Equilibrium Problems

More information

International Journal of Mathematical Archive-7(1), 2016, Available online through ISSN

International Journal of Mathematical Archive-7(1), 2016, Available online through   ISSN International Journal of Mathematical Archive-7(1), 2016, 200-208 Available online through www.ijma.info ISSN 2229 5046 ON ANTI FUZZY IDEALS OF LATTICES DHANANI S. H.* Department of Mathematics, K. I.

More information

Order-theoretical Characterizations of Countably Approximating Posets 1

Order-theoretical Characterizations of Countably Approximating Posets 1 Int. J. Contemp. Math. Sciences, Vol. 9, 2014, no. 9, 447-454 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2014.4658 Order-theoretical Characterizations of Countably Approximating Posets

More information

Formula for Lucas Like Sequence of Fourth Step and Fifth Step

Formula for Lucas Like Sequence of Fourth Step and Fifth Step International Mathematical Forum, Vol. 12, 2017, no., 10-110 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.612169 Formula for Lucas Like Sequence of Fourth Step and Fifth Step Rena Parindeni

More information

Continuity of Darboux Functions

Continuity of Darboux Functions International Mathematical Forum, Vol. 8, 2013, no. 16, 783-788 HIKARI Ltd, www.m-hikari.com Continuity of Darboux Functions Nikita Shekutkovski Ss. Cyril and Methodius University, Skopje, Republic of

More information

On Regular Prime Graphs of Solvable Groups

On Regular Prime Graphs of Solvable Groups International Journal of Algebra, Vol. 10, 2016, no. 10, 491-495 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ija.2016.6858 On Regular Prime Graphs of Solvable Groups Donnie Munyao Kasyoki Department

More information

Some Properties of a Semi Dynamical System. Generated by von Forester-Losata Type. Partial Equations

Some Properties of a Semi Dynamical System. Generated by von Forester-Losata Type. Partial Equations Int. Journal of Math. Analysis, Vol. 7, 2013, no. 38, 1863-1868 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2013.3481 Some Properties of a Semi Dynamical System Generated by von Forester-Losata

More information